Roughness Coefficient
Consider water is fully flowing 0.75 ft/s through a 0.25 foot diameter pipe at a 10% slope. What is the pipe’s roughness coefficient?
Expand Hint
Manning’s equation:
$$$V=\frac{K}{n}R_{H}^{2/3}S^{1/2}$$$
where
$$V$$
is the velocity,
$$K=1.486$$
for USCS units,
$$n$$
is the roughness coefficient,
$$R_H$$
is the hydraulic radius, and
$$S$$
is the slope.
Hint 2
To find hydraulic radius:
$$$R_H=\frac{A}{P}$$$
where
$$A$$
is the area, and
$$P$$
is the perimeter.
Manning’s equation:
$$$V=\frac{K}{n}R_{H}^{2/3}S^{1/2}$$$
where
$$V$$
is the velocity,
$$K=1.486$$
for USCS units,
$$n$$
is the roughness coefficient,
$$R_H$$
is the hydraulic radius, and
$$S$$
is the slope. To find hydraulic radius:
$$$R_H=\frac{A}{P}$$$
where
$$A$$
is the area, and
$$P$$
is the perimeter. Thus, the hydraulic radius is:
$$$R_H=\frac{(\pi/4)(D^2) }{(\pi D)}=\frac{D}{4}=\frac{0.25ft}{4}=0.0625\:ft$$$
To find the roughness coefficient:
$$$0.75\frac{ft}{sec}=\frac{1.486}{n}(0.0625m)^{2/3}\sqrt{10/100}$$$
$$$n=\frac{1.486}{0.75}(0.157)(0.316)=0.099=0.1$$$
0.1
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